math-float64-epsilon-difference
v1.0.0
Published
Computes the relative difference of two real numbers in units of double-precision floating-point epsilon.
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Relative Difference
Computes the relative difference of two real numbers in units of double-precision floating-point epsilon.
Installation
$ npm install math-float64-epsilon-difference
Usage
var diff = require( 'math-float64-epsilon-difference' );
diff( x, y[, scale] )
Computes the relative difference of two real numbers in units of double-precision floating-point epsilon.
var d = diff( 12.15, 12.149999999999999 );
// returns ~0.658ε
The following scale
functions are supported:
- max-abs: maximum absolute value of
x
andy
(default). - max: maximum value of
x
andy
. - min-abs: minimum absolute value of
x
andy
. - min: minimum value of
x
andy
. - mean-abs: arithmetic mean of the absolute values of
x
andy
. - mean: arithmetic mean of
x
andy
. - x:
x
(noncommutative). - y:
y
(noncommutative).
By default, the function
scales the absolute difference by dividing the absolute difference by the maximum absolute value of x
and y
. To scale by a different function
, specify a scale function name.
var d = diff( 2.4341309458983933, 2.4341309458633909, 'mean-abs' );
// returns ~64761.5ε => ~1.438e-11
To use a custom scale function
, provide a function
which accepts two numeric arguments x
and y
.
function scale( x, y ) {
// Return the minimum value:
return ( x > y ) ? y : x;
}
var d = diff( 1.0000000000000002, 1.0000000000000100, scale );
// returns ~44ε
Notes
If computing the relative difference in units of epsilon will result in overflow, the function returns the maximum double-precision floating-point number.
var d = diff( 1e304, 1, 'min' ); // returns ~1.798e308ε => 1e304/ε overflows
If the absolute difference of
x
andy
is0
, the relative difference is always0
.var d = diff( 0, 0 ); // returns 0ε d = diff( 3.14, 3.14 ); // returns 0ε
If
|x| = |y| = infinity
, the function returnsNaN
.var PINF = Number.POSITIVE_INFINITY; var NINF = Number.NEGATIVE_INFINITY; var d = diff( PINF, PINF ); // returns NaN d = diff( NINF, NINF ); // returns NaN
If
|x| = |-y| = infinity
, the relative difference is+infinity
.var PINF = Number.POSITIVE_INFINITY; var NINF = Number.NEGATIVE_INFINITY; var d = diff( PINF, NINF ); // returns +infinity d = diff( NINF, PINF ); // returns +infinity
If a
scale
function returns0
, the function returnsNaN
.var d = diff( -1, 1, 'mean' ); // returns NaN => |2/0|
Examples
var EPS = require( 'const-eps-float64' );
var diff = require( 'math-float64-epsilon-difference' );
var sign;
var x;
var y;
var d;
var i;
for ( i = 0; i < 100; i++ ) {
x = Math.random();
sign = ( Math.random() > 0.5 ) ? 1 : -1;
y = x + sign*EPS*i;
d = diff( x, y );
console.log( 'x = %d. y = %d. d = %dε.', x, y, d );
}
To run the example code from the top-level application directory,
$ node ./examples/index.js
Tests
Unit
This repository uses tape for unit tests. To run the tests, execute the following command in the top-level application directory:
$ make test
All new feature development should have corresponding unit tests to validate correct functionality.
Test Coverage
This repository uses Istanbul as its code coverage tool. To generate a test coverage report, execute the following command in the top-level application directory:
$ make test-cov
Istanbul creates a ./reports/coverage
directory. To access an HTML version of the report,
$ make view-cov
Browser Support
This repository uses Testling for browser testing. To run the tests in a (headless) local web browser, execute the following command in the top-level application directory:
$ make test-browsers
To view the tests in a local web browser,
$ make view-browser-tests
License
Copyright
Copyright © 2016. The Compute.io Authors.